3D reconstruction for partial data electrical impedance tomography using a sparsity prior

Henrik Garde, Kim Knudsen

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Abstract

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent results for the 2D problem to 3D: prior information about the sparsity and spatial distribution of the conductivity is used to improve reconstructions for the partial data problem with Cauchy data measured only on a subset of the boundary. A sparsity prior is enforced using the ℓ1 norm in the penalty term of a Tikhonov functional, and spatial prior information is incorporated by applying a spatially distributed regularization parameter. The optimization problem is solved numerically using a generalized conditional gradient method with soft thresholding. Numerical examples show the effectiveness of the suggested method even for the partial data problem with measurements affected by noise.
Original languageEnglish
Title of host publicationProceedings of the 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (2014)
PublisherAmerican Institute of Mathematical Sciences (AIMS)
Publication date2015
Pages495-504
DOIs
Publication statusPublished - 2015
Event10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (2014) - Madrid, Spain
Duration: 7 Jul 201411 Jul 2014
Conference number: 10
https://www.aimsciences.org/conferences/2014/

Conference

Conference10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (2014)
Number10
CountrySpain
CityMadrid
Period07/07/201411/07/2014
Internet address

Cite this

Garde, H., & Knudsen, K. (2015). 3D reconstruction for partial data electrical impedance tomography using a sparsity prior. In Proceedings of the 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications (2014) (pp. 495-504). American Institute of Mathematical Sciences (AIMS). https://doi.org/10.3934/proc.2015.0495